Mathematical and Statistical Analysis of Doubling Times to Investigate the Early Spread of Epidemics: Application to the COVID-19 Pandemic
Mathematical and Statistical Analysis of Doubling Times to Investigate the Early Spread of Epidemics: Application to the COVID-19 Pandemic
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DOI：
10.3390/math9060625
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发表时间：
2021-03-01
期刊：
影响因子：
2.4
通讯作者：
Chowell, Gerardo
中科院分区：
文献类型：
--
作者：
Smirnova, Alexandra;DeCamp, Linda;Chowell, Gerardo
需要使用简单的数学工具来量化新出现和再次出现的传染病暴发所构成的威胁，使用捕捉暴发轨迹的最小数据。在这里，我们使用数学分析、模拟和新冠肺炎疫情数据来演示一种新的方法来数值和数学地刻画流行病的加倍时间随时间变化的速率。为此，我们分析了最初流行阶段的流行病倍增时间的动态，定义为累积发病率倍增的时间序列。我们引入了新的方法来描述流行病威胁，通过分析流行病的演变作为(1)流行病加倍的次数达到流行病峰值的次数和(2)加倍次数的增加速度来描述流行病威胁。在我们的倍增方法中，最危险的流行病威胁的规模增加了许多倍，倍增时间以相对较低的速度变化(例如，倍增时间几乎保持不变)，而最不容易传播的威胁只增加了几倍，倍增时间在出现期间迅速增加。我们推导了分析公式，并使用合成数据和新冠肺炎疫情数据对我们的方法进行了测试和说明。我们的数学分析表明，流行病倍增时间序列近似地按指数函数增加，其速率量化倍增时间的变化率。我们的解析结果与数值结果吻合得很好。我们的方法提供了一种简单而直观的方法，依靠最小的爆发轨迹数据来表征新出现和重新出现的传染病构成的威胁。
Simple mathematical tools are needed to quantify the threat posed by emerging and re-emerging infectious disease outbreaks using minimal data capturing the outbreak trajectory. Here we use mathematical analysis, simulation and COVID-19 epidemic data to demonstrate a novel approach to numerically and mathematically characterize the rate at which the doubling time of an epidemic is changing over time. For this purpose, we analyze the dynamics of epidemic doubling times during the initial epidemic stage, defined as the sequence of times at which the cumulative incidence doubles. We introduce new methodology to characterize epidemic threats by analyzing the evolution of epidemics as a function of (1) the number of times the epidemic doubles until the epidemic peak is reached and (2) the rate at which the doubling times increase. In our doubling-time approach, the most dangerous epidemic threats double in size many times and the doubling times change at a relatively low rate (e.g., doubling times remain nearly invariant) whereas the least transmissible threats double in size only a few times and the doubling times rapidly increases in the period of emergence. We derive analytical formulas and test and illustrate our methodology using synthetic and COVID-19 epidemic data. Our mathematical analysis demonstrates that the series of epidemic doubling times increase approximately according to an exponential function with a rate that quantifies the rate of change of the doubling times. Our analytic results are in excellent agreement with numerical results. Our methodology offers a simple and intuitive approach that relies on minimal outbreak trajectory data to characterize the threat posed by emerging and re-emerging infectious diseases.